SOLUTION: What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse: x^2/9 + y^2/16 =1

Question 936512: What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse:
x^2/9 + y^2/16 =1

Found 2 solutions by lwsshak3, MathLover1:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
What are the coordinates of the center, the lengths of the major and minor axes, vertices, co-vertices, and foci for each ellipse:
x^2/9 + y^2/16 =1
Given ellipse has a vertical major axis:
Its standard form of equation: , a>b, (h,k)=coordinates of center
..
For given ellipse:
center:(0,0)
a^2=16
a=4
length of major axis=2a=8
b^2=9
b=3
length of minor axis=2b=6
vertices:(0,0�a)=(0,0�4)=(0,-4) and (0,4)
co-vertices:(0�b,0)=(0�3,0)=(-3,0) and (3,0)
foci:
c^2=a^2-b^2=16-9=7
c=√7≈2.6
foci:(0,0�c)=(0,0�2.6)=(0,-2.6) and (0,2.6)

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The standard form of the equation of an ellipse is:
for horizontal ellipses, and
for vertical ellipses
In these equations, the "" and the "" are the and coordinates, respectively, of the center.
here is your ellipse:

from given we know that , ; so, center is at origin (,)
we also know that major axis is vertical and
semi-major axis length is
semi-minor axis length is
the vertices will be "" distance above and below the center:
vertices (, ) | (,)
The co-vertices are right and left:
(,) | (,)
The distance from the center to each focus is called "". The "" is not in the standard form of the equation for an ellipse. But there is a fixed relationship between the "", the "" and the "" values:

foci: | (, ) | (, )
or approximately (, ) | (, )

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